Subgroups — C₂×#30631522 #44552662

Order 32128.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₀₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#30631522	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₂₅₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₆×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₂₀₀₈	—	2	1	no	—
6	D₄₀₁₆	—	2	1	no	—
7	D₄₀₁₆	C₂²	1	2	yes	complemented
8	C₂₅₁⋊C₃₂	C₂²	1	2	yes	complemented
9	C₂×D₈×C₂₅₁	—	2	1	no	—
10	D₁₆×C₂₅₁	—	2	1	no	—
11	D₁₆×C₂₅₁	C₂²	1	2	yes	complemented
12	C₂×C₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
13	C₂×D₁₀₀₄	—	4	1	no	—
14	D₂₀₀₈	—	2	2	no	—
15	D₂₀₀₈	—	4	1	no	—
16	C₂×D₄×C₂₅₁	—	4	1	no	—
17	D₈×C₂₅₁	—	2	2	no	—
18	D₈×C₂₅₁	—	4	1	no	—
19	C₂×C₈×C₂₅₁	D₄	1	1	yes	characteristic
20	C₁₆×C₂₅₁	D₄	1	1	yes	characteristic
21	C₁₆×C₂₅₁	C₂³	1	1	yes	characteristic
22	C₂²×D₂₅₁	—	8	1	no	—
23	D₁₀₀₄	—	4	2	no	—
24	D₁₀₀₄	—	8	1	no	—
25	C₂³×C₂₅₁	—	8	1	no	—
26	D₄×C₂₅₁	—	4	2	no	—
27	D₄×C₂₅₁	—	8	1	no	—
28	C₂×C₄×C₂₅₁	D₈	1	1	yes	characteristic
29	C₈×C₂₅₁	D₈	1	1	yes	characteristic
30	C₈×C₂₅₁	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₂₅₁	—	8	2	no	—
32	C₂²×C₂₅₁	—	16	2	no	—
33	C₂²×C₂₅₁	D₁₆	1	1	yes	characteristic
34	C₂×D₂₅₁	—	8	2	no	—
35	C₂×D₂₅₁	—	16	2	no	—
36	C₄×C₂₅₁	D₁₆	1	1	yes	characteristic
37	C₄×C₂₅₁	C₂×D₈	1	1	yes	characteristic
38	C₂×C₂₅₁	—	16	2	no	—
39	C₂×C₂₅₁	D₃₂	1	2	yes	complemented
40	C₂×C₂₅₁	C₂×D₁₆	1	1	yes	characteristic
41	D₂₅₁	—	16	2	no	—
42	C₂₅₁	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
43	C₂×D₃₂	—	251	1	no	maximal, Sylow
44	C₂×D₁₆	—	251	1	no	—
45	C₂×D₁₆	D₂₅₁	1	1	yes	characteristic, complemented
46	D₃₂	—	251	4	no	—
47	C₂×C₃₂	—	251	1	no	—
48	C₂×D₈	—	2	1	no	—
49	C₂×D₈	—	502	1	no	—
50	D₁₆	—	2	1	no	—
51	D₁₆	—	502	1	no	—
52	D₁₆	—	251	2	no	—
53	D₁₆	C₂×D₂₅₁	1	2	yes	complemented
54	C₂×C₁₆	C₂×D₂₅₁	1	1	yes	characteristic
55	C₃₂	—	251	2	no	—
56	C₂×D₄	—	4	1	no	—
57	C₂×D₄	—	1004	1	no	—
58	D₈	—	2	2	no	—
59	D₈	—	4	1	no	—
60	D₈	—	1004	1	no	—
61	D₈	—	502	2	no	—
62	C₂×C₈	C₂²⋊D₂₅₁	1	1	yes	characteristic
63	C₁₆	C₂²⋊D₂₅₁	1	1	yes	characteristic
64	C₁₆	C₂²×D₂₅₁	1	1	yes	characteristic
65	C₂³	—	8	1	no	—
66	C₂³	—	2008	1	no	—
67	D₄	—	4	2	no	—
68	D₄	—	8	1	no	—
69	D₄	—	2008	1	no	—
70	D₄	—	1004	2	no	—
71	C₂×C₄	#16860795	1	1	yes	characteristic
72	C₈	#16860795	1	1	yes	characteristic
73	C₈	C₂×C₂²⋊D₂₅₁	1	1	yes	characteristic
74	C₂²	—	8	2	no	—
75	C₂²	—	16	2	no	—
76	C₂²	—	4016	2	no	—
77	C₂²	—	2008	2	no	—
78	C₂²	#22548656	1	1	yes	characteristic
79	C₄	#22548656	1	1	yes	characteristic
80	C₄	C₂×#16860795	1	1	yes	characteristic
81	C₂	—	16	2	no	—
82	C₂	—	4016	2	no	—
83	C₂	#30631522	1	2	yes	direct product factor
84	C₂	C₂×#22548656	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22548656
commutator, cosocle	C₁₆×C₂₅₁	C₂³
Frattini	C₁₆	C₂²×D₂₅₁
Fitting	C₂×D₁₆×C₂₅₁	C₂
socle	C₂²×C₂₅₁	D₁₆
hypercenter	C₂×D₁₆	D₂₅₁
hypocenter	C₂₅₁	C₂×D₃₂
LCS	G ▷ C₁₆×C₂₅₁ ▷ C₈×C₂₅₁ ▷ C₄×C₂₅₁ ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×D₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×D₄₀₁₆	C₂	semidirect
2. #30631522	C₂	direct (N × H)
3. C₂×C₂₅₁⋊C₃₂	C₂	semidirect
4. C₂×D₁₆×C₂₅₁	C₂	semidirect
7. D₄₀₁₆	C₂²	semidirect
8. C₂₅₁⋊C₃₂	C₂²	semidirect
11. D₁₆×C₂₅₁	C₂²	semidirect
39. C₂×C₂₅₁	D₃₂	semidirect
42. C₂₅₁	C₂×D₃₂	semidirect
45. C₂×D₁₆	D₂₅₁	semidirect
53. D₁₆	C₂×D₂₅₁	semidirect
83. C₂	#30631522	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×D₄₀₁₆	2
#30631522	2
C₂×C₂₅₁⋊C₃₂	2
C₂×D₁₆×C₂₅₁	2
C₂×D₃₂	251

Subgroups — C2×#30631522 #44552662

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#30631522 #44552662